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Article: Four-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi–Pasta–Ulam–Tsingou recurrence

TitleFour-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi–Pasta–Ulam–Tsingou recurrence
Authors
Issue Date2021
PublisherAmerican Institute of Physics. The Journal's web site is located at http://chaos.aip.org/chaos/staff.jsp
Citation
Chaos, 2021, v. 31 n. 8, p. article no. 083117 How to Cite?
AbstractModulation instability, breather formation, and the Fermi–Pasta–Ulam–Tsingou recurrence (FPUT) phenomena are studied in this article. Physically, such nonlinear systems arise when the medium is slightly anisotropic, e.g., optical fibers with weak birefringence where the slowly varying pulse envelopes are governed by these coherently coupled Schrödinger equations. The Darboux transformation is used to calculate a class of breathers where the carrier envelope depends on the transverse coordinate of the Schrödinger equations. A “cascading mechanism” is utilized to elucidate the initial stages of FPUT. More precisely, higher order nonlinear terms that are exponentially small initially can grow rapidly. A breather is formed when the linear mode and higher order ones attain roughly the same magnitude. The conditions for generating various breathers and connections with modulation instability are elucidated. The growth phase then subsides and the cycle is repeated, leading to FPUT. Unequal initial conditions for the two waveguides produce symmetry breaking, with “eye-shaped” breathers in one waveguide and “four-petal” modes in the other. An analytical formula for the time or distance of breather formation for a two-waveguide system is proposed, based on the disturbance amplitude and instability growth rate. Excellent agreement with numerical simulations is achieved. Furthermore, the roles of modulation instability for FPUT are elucidated with illustrative case studies. In particular, depending on whether the second harmonic falls within the unstable band, FPUT patterns with one single or two distinct wavelength(s) are observed. For applications to temporal optical waveguides, the present formulation can predict the distance along a weakly birefringent fiber needed to observe FPUT.
Persistent Identifierhttp://hdl.handle.net/10722/307614
ISSN
2023 Impact Factor: 2.7
2023 SCImago Journal Rankings: 0.778
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorYin, H-
dc.contributor.authorPan, Q-
dc.contributor.authorChow, KW-
dc.date.accessioned2021-11-12T13:35:11Z-
dc.date.available2021-11-12T13:35:11Z-
dc.date.issued2021-
dc.identifier.citationChaos, 2021, v. 31 n. 8, p. article no. 083117-
dc.identifier.issn1054-1500-
dc.identifier.urihttp://hdl.handle.net/10722/307614-
dc.description.abstractModulation instability, breather formation, and the Fermi–Pasta–Ulam–Tsingou recurrence (FPUT) phenomena are studied in this article. Physically, such nonlinear systems arise when the medium is slightly anisotropic, e.g., optical fibers with weak birefringence where the slowly varying pulse envelopes are governed by these coherently coupled Schrödinger equations. The Darboux transformation is used to calculate a class of breathers where the carrier envelope depends on the transverse coordinate of the Schrödinger equations. A “cascading mechanism” is utilized to elucidate the initial stages of FPUT. More precisely, higher order nonlinear terms that are exponentially small initially can grow rapidly. A breather is formed when the linear mode and higher order ones attain roughly the same magnitude. The conditions for generating various breathers and connections with modulation instability are elucidated. The growth phase then subsides and the cycle is repeated, leading to FPUT. Unequal initial conditions for the two waveguides produce symmetry breaking, with “eye-shaped” breathers in one waveguide and “four-petal” modes in the other. An analytical formula for the time or distance of breather formation for a two-waveguide system is proposed, based on the disturbance amplitude and instability growth rate. Excellent agreement with numerical simulations is achieved. Furthermore, the roles of modulation instability for FPUT are elucidated with illustrative case studies. In particular, depending on whether the second harmonic falls within the unstable band, FPUT patterns with one single or two distinct wavelength(s) are observed. For applications to temporal optical waveguides, the present formulation can predict the distance along a weakly birefringent fiber needed to observe FPUT.-
dc.languageeng-
dc.publisherAmerican Institute of Physics. The Journal's web site is located at http://chaos.aip.org/chaos/staff.jsp-
dc.relation.ispartofChaos-
dc.rightsChaos. Copyright © American Institute of Physics.-
dc.rightsAfter publication please use: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in (citation of published article) and may be found at (URL/link for published article abstract). Prior to publication please use: The following article has been submitted to/accepted by [Name of Journal]. After it is published, it will be found at Link. For Creative Commons licensed material, please use: Copyright (year) Author(s). This article is distributed under a Creative Commons Attribution (CC BY) License.-
dc.titleFour-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi–Pasta–Ulam–Tsingou recurrence-
dc.typeArticle-
dc.identifier.emailYin, H: hmy63110@hku.hk-
dc.identifier.emailPan, Q: panqing@hku.hk-
dc.identifier.emailChow, KW: kwchow@hku.hk-
dc.identifier.authorityChow, KW=rp00112-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1063/5.0051584-
dc.identifier.pmid34470240-
dc.identifier.scopuseid_2-s2.0-85113169271-
dc.identifier.hkuros329515-
dc.identifier.volume31-
dc.identifier.issue8-
dc.identifier.spagearticle no. 083117-
dc.identifier.epagearticle no. 083117-
dc.identifier.isiWOS:000684667100001-
dc.publisher.placeUnited States-

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